Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#5066 |
| Fitting | C2×C3×#125 ⋊ C2 |
| Sylow | C3 ⋊ C2×#478 |
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7,9,11)(8,13,12,10)(14,16,17,21)(15,18,19,20);(1,2)(7,11)(10,13)(14,15,17,19)(16,20,21,18);(4,5)(7,10)(8,12)(11,13);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10691533, #10691539, C4×#5066, … |
| maximal normal subgroup of | #10691533, #10691539, C4×#5066, … |
| maximal quotient of | C2×#69556, C2×#69625, C2×#69626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15592);